Getting no output sounds like something is wrong, like maybe the parts are defective. Hopefully you purchased them from a reliable source.
They're not exact replacements because they can withstand less input voltage (30V rather than 35V) and they draw rather nasty amounts of Iq (as much as 100mA typical) when the output current is high and the regulator is dropping out (this hideous behavior is typical of such antediluvian regulators made with low-hFE lateral PNP pass transistors).
I suppose it's possible this is causing your source to current limit and restart, resulting in an endless loop.
They don't say so in the datasheet but the regulator is probably not guaranteed stable with ceramic output caps, and needs a fat-ish 22uF or more aluminum electrolytic or tantalum cap with relatively high ESR on the output. The LM7805 is much more forgiving.
There's no power dissipation advantage in dropping one of these in place of a 7805, not at all, under some conditions just the opposite. There are switching regulators that you can use such as the Murata OKI-78SR-5/1.5-W36-C which actually are very efficient and are (more-or-less) drop-in replacements allowing you to leave off the heatsink.
Be sure to read the datasheet.